切变Turbulence中尘埃层的长期重力不稳定性
Secular Gravitational Instability of a Dust Layer in Shear Turbulence
摘要：
本文对湍流气盘中的尘埃层进行了线性稳定性分析。Youdin（2011）使用带有湍流扩散项的流体动力学方程研究了尘埃层的长期引力不稳定性。我们独立于Youdin（2011）获得了基本相同的结果。在目前的分析中，我们将感兴趣的区域限制在小尘埃颗粒上，同时以更严格的方式研究长期的引力不稳定性。我们讨论了沙尘表面密度分布的时间演化的随机模型，并推导出对流扩散方程。Youdin（2011）分析的有效性在强阻力极限中得到了证实。我们定量地证明了尘埃层的有限厚度减弱了长期的引力不稳定性，密度依赖的扩散系数改变了增长率。将所得结果应用于剪切不稳定性驱动的湍流，发现当气体密度为最小质量圆盘模型的3倍时，长期引力不稳定性比径向漂移更快。如果尘埃颗粒比球粒大，长期的引力不稳定性在原行星盘的寿命内增长。
英文摘要：
We perform a linear stability analysis of a dust layer in a turbulent gas disk. Youdin (2011) investigated the secular gravitational instability of a dust layer using hydrodynamic equations with a turbulent diffusion term. We obtain essentially the same result independently of Youdin (2011). In the present analysis, we restrict the area of interest to small dust particles, while investigating the secular gravitational instability in a more rigorous manner. We discuss the time evolution of the dust surface density distribution using a stochastic model and derive the advection-diffusion equation. The validity of the analysis by Youdin (2011) is confirmed in the strong drag limit. We demonstrate quantitatively that the finite thickness of a dust layer weakens the secular gravitational instability and that the density-dependent diffusion coefficient changes the growth rate. We apply the obtained results to the turbulence driven by the shear instability and find that the secular gravitational instability is faster than the radial drift when the gas density is three times as large as that in the minimum-mass disk model. If the dust particles are larger than chondrules, the secular gravitational instability grows within the lifetime of a protoplanetary disk.
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